Synchro servosystem in which a potentiometer with unique characteristics replaces the receiver

ABSTRACT

Potentiometer structures for synchro systems and synchro systems utilizing such structures. One or more potentiometers are employed in place of the usual rotor and stator inductive transformer arrangements employed in the control transmitter and control transformer of a synchro system. The potentiometer employed in the synchro control transformer has a resistivity which varies in accordance with a cotangent function of the displacement of the movable wiper of the potentiometer from a reference position. Essentially the control transformer potentiometer employs three similar resistive segments, each corresponding to 120 electrical degrees of rotation of the potentiometer. The equation expressing the resistance R at a location in a segment as a function of the angle of displacement is as follows: R ( 1/2 -( 3/6)ctn.(30*+X))Rt WHERE X equals the electrical angle of displacement which, for each segment, varies from 0* to 120*, and Rt is the open circuit resistance between the ends of each segment. The potentiometer employed as a synchro control transmitter to be used with the potentiometer-type synchro control transformer just described includes a square-shaped film of uniform resistivity against which bear three wipers of equal angular separation (120*). The wipers provide the output signal to the control transformer. The input to the square-shaped film is an AC or DC signal applied to opposing sides of the film. A midpoint of one or both of the two remaining sides is typically grounded. The signals from the three wipers are related to the DC input signal by a sine function, i.e., dependent upon the sine of the angle of rotation of the wipers from a reference position.

United States Patent Yanosik [54] SYNCHRO SERVOSYSTEM IN WHICH APOTENTIOMETER WITH UNIQUE CHARACTERISTICS REPLACES THE RECEIVER [72]lnventor: Joseph J. Yanoslk, Huntington Station,

Long Island, NY.

[73] Assignee: Betatronlx, Inc., East Northport, NY. [22] Filed: Mar.20, 1968 [21] App]. No.1 714,684

Primary Examiner-T. E. Lynch Attorney-Robert S. Dunham, P. E. Henninger,Lester W.

1451 Jan. 18, 1972 [57] ABSTRACT Potentiometer structures for synchrosystems and synchro systems utilizing such structures. One or moreotentiometers are employed in place of the usual rotor and statorinductive transformer arrangements employed in the control transmitterand control transformer of a synchro system. The potentiometer employedin the synchro control transformer has a resistivity which varies inaccordance with a cotangent function of the displacement of the movablewiper of the potentiometer from a reference position. Essentially thecontrol transformer potentiometer employs three similar resistivesegments, each corresponding to I20 electrical degrees of rotation ofthe potentiometer. The equation expressing the resistance R at alocation in a segment as a function of the angle of displacement is asfollows:

R= 1/2- View. 30+ X)]R,

where X equals the electrical angle of displacement which, for eachsegment, varies from 0 to 120, and R, is the open circuit resistancebetween the ends of each segment.

The potentiometer employed as a synchro control transmitter to be usedwith the potentiometer-type synchro control transformer just describedincludes a squareshaped film of uniform resistivity against which bearthree wipers of equal angular separation (120). The wipers provide theoutput signal to the control transformer. The input to the square-shapedfilm is an AC or DC signal applied to opposing sides of the film. Amidpoint of one or both of the two remaining sides is typicallygrounded. The signals from the three wipers are related to the DC 'inputsignal by a sine function, i.e., dependent upon the sine of the angle ofrotation of the wipers from a reference position.

Clark, Thomas F. Moran, Gerald W. Griffin, Howard J.8Claims,9DrawingFigureS Churchill, R. Bradlee Boal, ChristopherC. Dunhamand Robert Scobey AA/TE/V/t A .5? .24 J /-a4a f /0 S V/t/CHAO U 994 5 315 4 544 5 44..

i 20 5YA/C/7,0 2 1 GOA T201. OUTP T r/eAus/ o/wfz 1 H l I I 1 V 1 i ERR'95 5661 4 l 'T m Luca r 6 INPUT H VOLTAGE H PATENTED JAN 1 8 I972 SHEET3 0F 3 UN/FOP/V FILM INVENTOR. JOSEPH J K /vos/x BY EM filly BACKGROUNDAND BRIEF DESCRIPTION OF THE INVENTION This invention relates topotentiometer structures, andparticularly to potentiometer structuressuitable for replacing the rotor and stator transformer coilarrangements found in synchro systems.

A synchro system is a system for positioning a movable object inaccordance with the position of a control mechanism, commonly termed asynchro control transmitter. In the past the synchro control transmitterhas been a transformer arrangement formed from three fixed stator coilsand one movable rotor coil. The position of the rotor coil inducesvarying voltages in the three stator coils. In the past thesestator'coils have been coupled to three similar stator coils in asynchro control transformer which includes a movable rotor coupled tothe movable object whose position is to be determined by the movement ofthe rotor of the synchrocontrol transmitter. The signal applied to thesynchro control transmitter rotor and the signal induced in the rotor ofthe synchro control transformer are applied to a phase-sensitiveamplifier. An output signal is developed which is used to drive aservomotor which moves the movable object. Because of the externalmechanical coupling between this object and the rotor of the synchrocontrol transformer the rotor is moved until the signal therefrom iszero indicating that this rotor is in the same relative position as therotor of the synchro controltransmitter. The difference in phase betweenthe signals applied to the amplifier determines the direction ofmovement of the servomotor. Y

As indicated, it has been common in the past to employ inductive"-typedevices for the synchro control transmitter and synchro controltransformer. There are many applications, however, because of spacelimitations, e.g., which render impractical the use of inductive-typedevices. The present invention is directed to the use of potentiometerstructures to replacethe conventional inductive-type devices used in thepast.

A potentiometer structure is required which will simulate aninductive-type device, so that, e.g., a synchro control transformer maybe a potentiometer whichreceives a signal from a conventional synchrocontrol transmitter employing conventional-type coils. By the sametoken, it is desirable to provide a potentiometer for a synchro controltransmitter which simulates the signals produced by the conventionalcoil type arrangement so that these signals may be applied to a synchrocontrol transformer employing a potentiometer rather than coil-typearrangement.

It has been found in the present invention that, as far as the synchrocontrol transformer is concerned, a potentiometer can be constructed tosimulate the action of the conventional coil type arrangement. It hasbeen discovered that the resistivity should vary in accordance with acotangent function dependent upon the electrical angle of displacementwith respect to a reference 'position. On the other hand, in apotentiometer for a synchro control transmitter, it has been discoveredthat a square-shaped film of uniform resistance should be used inconjunction with three wipers spaced 120 electrical degrees from eachother. An AC or DC input signal is applied to the film to generatesignals from the wipers varying in accordance with the sine of the angleof rotation of the wipers from a reference position.

The potentiometer structures proposed herein may be made relativelysmall so as to find application in instrument control systems and thelike Where space requirements are important. Further, the potentiometerspermit control by DC as well as AC signals (inductive-type transformersare limited to AC control signals), and calibration and adjustment iseasily accomplished through DC measurement. The potentiometers thusprovide a greater flexibility in use than transformers of the inductivetype.

BRIEF DESCRIPTION OF THE DRAWINGS The accompanying drawings illustraterepresentative embodiments of the invention.

FIG. I is a block diagram of a synchro system in accordance with theinvention.

FIG. 2 is a sideview of a potentiometer structure useful in the systemof FIG. 1 as a synchro control transformer.

FIGS. 3 and 4 are views of parts of the potentiometer structure of FIG,2, looking in the direction of the arrows 33 and 4-4 of FIG. 2.

FIG. 4a is a curve plotting the output signal from a wiper of thepotentiometer of FIG. 2 as a function of angular displacement of thewiper in degrees from a reference position.

FIG. 4b is a curve showing the thickness of a conductive plasticresistive film at any point in the film as a function of the angulardisplacement of that point from a reference position.

FIGS. 5 and 6 are views similar to FIGS. 3 and 4 showing an alternativepotentiometer structure suitable as a synchro control transformer inFIG. 1 and designed to provide twice the degree of movement of the rotorwith respect to movement of the synchro control transmitter rotor.

FIG. 7 is a view in schematic form of.a potentiometer structure suitableas a synchro control transmitter in the system of FIG. 1.

DETAILED DESCRIPTION Referring to FIG. 1, there is shown a synchrosystem in accordance with the invention. A conventional synchro controltransmitter 10 is shown having a rotor 12 which is energized by asuitable varying signal applied to a pair of of conductors 14. The rotor12 constitutes one coil of a transformer which is variable in positiontypically so as to rotate 360 about an axis. The angular position of therotor corresponds to the position of some mechanism to be adjusted, forexample, an antenna 16. To this end the synchro control transmitter 10includes three stator coils 18, 20 and 22 in which are inducedelectrical signals of a phase and magnitude in accordance with the angular position of rotor coil 12.

Signals from the stator coils 18, 20 and 22 are applied to a synchrocontrol transformer 24. Conventionally the synchro control transformeris a rotor coil and stator coil structure as is the control transformer10. However, in the present invention, the synchro control transformer24 is a potentiometer structure such as that shown in FIGS. 2 to 4, tobe described below. The synchro control transformer includes a rotorwhich produces an electrical signal on conductors 26 which is applied toan amplifier 28, typically a phase-sensitive amplifier. This amplifieralso receives as a reference input signal the signal on the conductors14 that energizes the synchro control transmitter rotor coil 12. Anypotential difference between the two conductors 26 from the controltransformer 24 causes an output signal to be generated on conductors 30from the amplifier which are connected to a servo motor 32. Thedifference in phase between the signals on the conductors 26 and 14determines the phase of the amplifier output signal and the direction ofrotation of the servomotor. The servomotor includes a shaft 34 whichdrives the antenna 16. The shaft 34 is coupled to a shaft 34a, in turncoupled to the rotor of the synchro control transformer 24. As energizedby a signal on the conductors 30, the servomotor 32 moves the antennaand hence the rotor of the synchro control transformer 24 until thesignal on the conductors 26 (the potential difference between theconductors) is zero. When this occurs, the rotor of the synchro controltransformer is in the same angular orientation with respect to areference position as is the rotor coil 12 in the synchro controltransmitter. The output signal on the conductors 30 from the amplifier28 drops to zero, stopping movement of the servomotor. In this fashion,the antenna is positioned in accordance with the position of the rotorcoil 12 of the synchro control transmitter.

As explained above, the synchro control transformer 24 is comprised of apotentiometer structure such as shown in FIGS. 2 to 4. A somewhatdifferent potentiometer structure is shown in FIGS. 5 and 6, and apotehtiometer structure suitable as a replacement for the coilarrangement of the synchro control transmitter is shown in FIG. 7. Thesepotentiometer structures will now be described in detail.

Referring to FIG. 2, the stator of the synchro control transformer 24comprises a platelike structure 36 fixed in position by a bracket 38.The rotor of the synchro control transformer is formed from anotherplatelike structure 40 having a hub 40a affixed to the shaft 34a that isconnected to the antenna structure 16 in FIG. 1. The shaft 34a thusrepresents the movable mechanism whose position is to be adjusted inaccordance with the position of the rotor coil 12 of the synchro controltransmitter 10.

Referring to FIG. 4, the stator 36 of the potentiometer structureincludes a resistive material 42 thereon. Typically this resistivematerial is in the form of a resistive film which is deposited on aplastic'base in accordance with conventional plastic film techniques.The resistive film 42 includes three segments 42a, 42b and 421:. Eachsegment constitutes I electrical degrees of rotation of thepotentiometer. In this potentiometer structure the potentiometer rotor40 is adapted to make one complete revolution for one completerevolution of the transmitter rotor 12in FIG. 1.

It will be noted that the shape of the resistive film 42 is not uniform.This is done so that the resistivity at any position in a film segmentis a function of the angular displacement of that position with respectto a reference position, as will be explained in more detail below. Theresistive film has three points of connection 44, 46 and 48, spaced theequivalent of 120 electrical degrees from each other. Conductors 44a,46a and 48a are connected to these points of connection to the resistivefilm. These conductors are designated by the same reference numerals inFIG. 1 and are shown connected to the synchro control transmitter coils18, 20 and 22. Two wipers 50 and 52 are positioned on the stator plate36, as shown in FIGS. 2 and 4, and bear respectively against conductivetracks 50a and 52a on the rotor plate 40 shown in FIG. 3. A wiper 52b iselectrically connected to the track 52a, and another wiper 50b isconnected to the track 50a. The wipers 50b and 52b are positioned I80electrical degrees from each other and bear against the resistive film42. Thus the wipers 50b and 52b pick off signals from the resistive film42 and transfer these signals to the conductive tracks 50a and 52a whichin turn transfer the signals to the wipers 50 and 52. The wipers 50 and52 are connected to conductors 26 which, as shown in FIG. 1, constitutethe synchro control transformer rotor conductors applying an errorsignal to the phase-sensitive amplifier 28. The wipers 50 and 52 arespaced so that the wipers 50b and 5211 may pass freely therebetween asthe potentiometer rotor 40 rotates.

As noted above, the configuration or shape of the resistive film 42varies in accordance with position at any point in the film from areference position. Specifically, each of the segments 42a, 42b and 420has the same resistivity characteristic as a function of position.Taking the potentiometer segment 42a as an example, and considering areference position of 20 degrees as passing through the point ofconnection 44, the resistivity R between the point of connection and oneof the wipers 50b and 52b at an angular displacement of X, degrees fromthe reference or zero position is given by the following equation:

R=[%-( 3/6) ctn. (30+X)]R,, (l) in which R, is the open circuitresistance between the points of connection 44 and 46 at the ends of thepotentiometer segment 42a.

It has been found that if the resistivity of each segment of theresistive film 42 varies in accordance with the above equation, signalswill be developed on the conductors 26 for varying positions of therotor the same as signals developed from a conventional rotor coil of aconventional coil-type synchro control transformer. In particular, thewipers 50b and 52!) pick off equal potentials (a zero signal from theresistive film 42 when the rotor 40 is displaced angularly from areference posi' tion corresponding to'the angular displacement of thetransmitter rotor from a reference position). Such a zero signal isdeveloped by the rotor coil of a conventional synchro controltransformer when in this same angular orientation, and hence thepotentiometer-type control transformer of the present invention maydirectly replace the conventional coil-type control transformer in asynchro system.

In practice, the variation of resistivity as a function of an gulardisplacement may be achieved by a number of different techniques. Afirst technique is to employ a resistive film 42 which is constant inthickness and uniform throughout the entire extent thereof except forthe shaping of the film by etching or otherwise so that it assumes theshape shown in FIG. 4. In this case the width of the film (in a radialdirection) varies in accordance with the angular displacement X. It ispossible to maintain the width of the film constant and to vary thethickness, for example, in order to achieve the appropriate resistivityvariation as a function of angular displacement. Other techniques are byvarying the width and thickness of the resistive film simultaneously, orby shunting various portions of the resistive film either with resistorsmounted external to the stator plate 36 or by the use of an overlay ofresistive material deposited selectively on various portions of thefilm. Another technique is to change the composition of the material forvarious positions in the film segments.

No matter which technique of resistance variation is employed, thefabrication of the potentiometer film 42 is easily accomplished byapplying a signal, for example, between the connection points 44 and 46and measuring the potential difference between the connection point 44and one of the wipers 50b and 52b (as measured at one of the conductors26) as that wiper is moved from adjacent connection point 44 on thesegment 42a to adjacent the connection point 46. The output signal thatshould be obtained (expressed as a fraction of the input signal appliedto the connection points 44 and 46) is shown in FIG. 4a, by the curvedesignated 60. In this regard, it is assumed that one of the wipers ismoving from adjacent the connection point 44 to adjacent the connectionpoint 46 and that the connection point 44 is grounded, for example, andthat a full input signal of L00 is applied to the connection point 46.The curve 60 is in the form of a cotangent function. As the wiper ismoved through the of displacement from adjacent the connection point 44to adjacent the connection point 46, the potentials indicated by thecurve 60 should be obtained. As shown in FIG. 4, the width of the filmmay be made to vary to achieve the appropriate relationship betweenresistivity and angular displacement. Depending upon the signalpotentials detected at the various angular positions, the film segment42a is appropriately changed in width to achieve the desiredrelationship. Conductive bits of material, for example, may also beapplied to the film to shunt various portions of the film to change theresistivity, if desired, so that the signal detected from the wiperfollows a curve such as curve 60 shown in FIG. 4.

In the same fashion, conductive segments 42b and 420 are shaped toprovide the appropriate resistivity variation as a function of angulardisplacement. The curve 62 in FIG. 4a shows the variation in signaldetected at one of the wipers that should be obtained as the wiper ismoved from adjacent the connection point 46 to adjacent the connectionpoint 48, with the point 46 having full input potential applied theretoand point 48 grounded, for example. Finally, the curve 64 in FIG. 4ashows the variation in signal from one of the wipers as the wiper ismoved over the resistive segment 42c from adjacent the connection point48 to adjacent the connection point 44, and with connection point 48being grounded and the full input signal being applied to connectionpoint 44.

FIG. 4b shows the variation of film thickness as a function of angulardisplacement in degrees to obtain the desired resistivity variation byvarying solely the thickness of the film and maintaining the widthconstant. It is indicated in FIG. 4b that the three taps or connectionpoints (corresponding to connection points 44, 46 and 48) are at 60, 180and 300 corresponding to points of minimum thickness.

As noted above, no matter how the resistivity is varied, the variationis in accordance with a cotangent function as noted above in equation(1). Because the synchro control transformer constitutes apotentiometer, the potentiometer may be fabricated by monitoring asignal, as explained above in connection with FIG. 4a, and varying theresistivity so that the proper signal is obtained as the potentiometerrotor is moved. It should be noted that when shape or configuration isvaried, such as by varying width or thickness or both, the variation atany point is determined from the derivative'of the resistivity equationl above.

Equation (1) above gives the relationship between resistivity andangular displacement in which a single complete rotation of the rotor 12of the synchro transmitter produces a single complete rotation of therotor 40 of the synchro receiver 24. With respect to equation (1), theelectrical zero position of the control transformer rotor 40 will beachieved when the following relationship exists between the angulardisplacement 8 of the control transmitter rotor 12 from a referenceposition and the angular displacement X of the control transformer rotor40 from a reference position.

kElO -X. (2) Equation (1) above may be generalized for the case in whichthe synchro transmitter rotor 12 rotates one complete revolution and thereceiver rotor 40 rotates a fraction of a revolution or some othernumber of revolutions. Equation (1 expressing resistivity R in eachsegment as a function of angular displacement X, is written for thegeneral case, as follows:

in which A is the ratio of the rotation of rotor to the rotation oftherotor 12. Specifically, equation (3) is as follows, when the controltransmitter rotor 12 makes one complete revolution and produces twocomplete revolutions of the control transformer rotor 40:

FIGS. 5 and 6 show potentiometer structures similar to that of FIGS. 2to 4, specifically designed to provide twice the degree of movement ofthe control transformer rotor with respect to movement of the controltransmitter rotor. FIG. 5 shows the rotor structure comprising a plate70 and conductive tracks 72a and 74a. Wipers 72b and 74b are connectedto the tracks directly adjacent each other, and these wipers in turnmake contact with resistivefilm sections or tracks on the statorstructure 80. Specifically, the stator structure includes an outsidesection or track 82 and an inside section or track 84 contactedrespectively by the wipers 72b and 74b. The resistive tracks 82 and 84vary in resistivity dependent upon displacement from a referenceposition in accordance with equation (4) above. The outside trackincludes spaced ends 82a and 82b, while the inside track includes spacedends 84a and 84b. The ends 82a and 84b are joined together by aconductor 88 and constitute one point of connection of the potentiometerstructure connected to a conductor 90. The ends 82b and 84a are alsoconnected together by a conductor 92. Other connection points are takenfrom the resistive film tracks as at a point 94 on the inner track 84(connected to a conductor 96) and at a point 98 connected to the outertrack 82 (in turn connected to a conductor 100). Wipers 102 and 104connected to conductors 106 and 108 make contact with the conductivetracks 72a and 74a of the rotor to transfer the signal picked off theresistive tracks by the wipers 72b and 74b as an output signal. In thisregard, the conductors 90, 96 and 100 correspond to conductors 44a, 46aand 48a in the system of FIG. 1, while the conductors 106 and 108correspond to the conductors 26 in the system of FIG. 1.

The connection points 88, 94 and 98 are spaced 120 electrical degreesform each other, although actually they are spaced 240 in rotation aswill be explained. Commencing from the connection point 98, travelingclockwise, the wiper 72b travels from adjacent this connection point onthe outer track 82 for 240 of rotation until the connection 88 isreached. For further clockwise rotation of the rotor 70, the inner wiper74b engages the inner track 84 for 240 of rotation until connectionpoint 94 is reached. Finally, continued clockwise rotation of the rotorprovides travel of the inner wiper 74b to the conductor 92 linking theends 84a and 82b of the inner and outer tracks, the outer wiper 72bmoves along the outer track 82 until 240 of rotation have been achieved,again back to the connection 98. Two complete revolutions of the wipersconstitute 360 electrical degrees. Although the connection points arespaced 240 physically, they are spaced 120 electrically. For this reasonthe two wipers 72b and 74b are spaced 180 electrically from each other,although physically the travel from one wiper to another constitutes afull 360 of rotor rotation.

It will be noted that at the region of the connection 88, there is adiscrete spacing between the ends of the inner and outer resistivetracks 82 and 84. As the outer wiper 72b passes from the end 82a to theend 82b, there is an abrupt change in resistivity. Similarly, as theinner wiper 74b passes from the end 84a to the end 84b, there is anotherabrupt change in resistivity. However, since the ends 84a and 82b arelinked together, as are the ends 82a and 84b, and since these linkedends have the same resistivity, there is essentially no abrupt change inresistivity between the wipers 72b and 74b or in the signal developedbetween the wipers. It is recognized that if the wipers fall inside theregion between the resistive tracks, there will be no engagement withthe tracks. This cannot be tolerated, and hence the potentiometer ofFIGS. 5 and 6 is used only in connection with mechanical stops (notshown) preventing travel of the wipers through the region between theresistive tracks. This limits the use of the potentiometer to a systemin which it rotates just short of 360, 'e.g., 350, corresponding to 175of rotation, e.g., of the control transmitter rotor.

The embodiments shown in FIGS. 2 to 6 have all involved rotationalmovement of the potentiometer. The invention is applicable to linearmovement or any movement other than rotational. Equation (1) above maybe further expanded for the general case involving any type of motion,as follows:

R==[ 3/6) ctn. (30+(AY/Y)l20)]R,, (5) where y,is the distance betweenadjacent connection points, and AY is the distance between a point atwhich the resistivity R is given and a reference point at an end of theresistive segment, and R, is the open circuit resistance between thesetwo connection points. It should be noted that two adjacent connectionpoints constitute 120 electrical degrees of potentiometer movement, andhence for a full 360 electrical degrees there should be a total of threeresistive segments, each segment the same as another segment, with theresistance of each segment varying in accordance with a referenceposition as in the above equation.

FIG. 7

FIG. 7 shows a potentiometer arrangement suitable for replacing thetransformer-type coils in the synchro transmitter 10. FIG. 7 has beendrawn schematically and involves a uniform film of resistive material101 against which bear three wipers 103, and 107. The wipers are drivenby a shaft 109 whose position with respect to a reference positiondetermines the movement of the antenna 16 in FIG. 1. Film 101 is squareshaped, and the wipers are equidistantly spaced 120 apart and are ofequal length. An AC or DC input potential is supplied between terminals110 and 112 connected respectively to conductive strips 114 and 116,which supply a potential gradient across the film. Typically, a midpoint117 of one or both of the other sides is grounded to provide a sinefunction signal from the potentiometer varying above and below ground.For an angle X of displacement with respect to a reference position, thepotential developed by the wiper 103 may be expressed as:

V =EsinX, (6) in which Y is the potential of wiper 103, Eis the inputsignal across the strips 114 and 116, and X is the angle ofdisplacement.

Similarly, for the same angular displacement, the potential of the wiper105 may be expressed as:

, V =E sin (X-HZO), 7 and the potential of the wiper 107 may beexpressed as:

V =E sin (X+240). (8) If these wipers are connected to the statorconnections of the synchro control transformer 24 in FIG. 1, anoperative synchro system will result. In this case the system mustemploy a potentiometer-type control transformer. A potentiometer for thesynchro control transmitter is not compatible with an inductivecoil-type control transformer.

SUMMARY A synchro system has been disclosed involving potentiometers toreplace the coil arrangements in the synchro control transmitter andcontrol transformer. While specific embodiments have been disclosed, itshould be understood that the invention is not limited to the specificembodiments, which are simply representative. The invention, therefore,should be taken to be defined by the following claims.

I claim:

1, In a synchro system that includes a synchro control transmitterhaving a stator with three stator outputs, the improvement comprising athree-region resistive material serving as and directly interchangeablewith a synchro control transformer and which is coupled to and energizedby the stator outputs and of a resistivity in each region which variesas a function of position within the region with respect to a referenceposition in accordance with a cotangent function.

2. A synchro system as defined in claim 1, wherein the stator comprisesa square-shaped resistive material, three wipers of equal lengthsconnected to and spaced 120 about an axis of rotation, the wipersconstituting the outputs of the stator, and means applying an inputsignal to two opposing sides of the square-shaped material.

3. A synchro system as defined in claim 2, wherein at least one of theremaining two sides of the square-shaped material is electricallygrounded.

4. A synchro system, comprising a synchro control transmitter having amovable rotor and three stator outputs, a potentiometer serving as anddirectly interchangeable with a synchro control transformer and whichcomprises a three-region resistive material, points of connection to theresistive material being coupled to the stator outputs of the synchrocontrol transmitter, a movable rotor forming part of the potentiometerand having two contacting means for engaging the resistive material atspaced points thereon so as to pick off the potentials of the engagedpoints of resistive material, the resistivity of the material varying ineach region as a function of position of the potentiometer rotor withrespect to a reference position and in accordance with a cotangentfunction so that the output potentials picked off by the contactingmeans are equal when the potentiometer rotor is in a position withrespect to a reference position corresponding to a similar position ofthe rotor of the synchro control transmitter with respect to a referenceposition in the control transmitter.

5. A synchro system as defined in claim 1, wherein the resistivematerial comprises a plurality of segments, each of which has the sameresistivity in accordance with a cotangent function as another segment.

6. A synchro system as defined in claim 1, wherein the re-I sistivity ofthe material is expressed substantially by the following formula:

=t cm. 9+X l wherein R IS the resistivity at a position in the material,X Is the displacement of this position in electrical degrees from areference position at an end of a segment of the material, which segmentrepresents electrical degrees, and R, is the open circuit resistancebetween the ends of the resistive segment.

7. A synchro system as defined in claim 6, wherein the resistivematerial is formed from three l20-electric'al-degree segments as definedin claim 22, the resistive material has three points of connectionthereto which are spaced 120 electrical degrees from each other, andthese three points of connection are coupled to the stator outputs ofthe synchro control transmitter.

8. A synchro system as defined in claim 7, including a rotor having twowipers contacting the resistive segments and which are spaced electricaldegrees from each other.

1. In a synchro system that includes a synchro control transmitter having a stator with three stator outputs, the improvement comprising a three-region resistive material serving as and directly interchangeable with a synchro control transformer and which is coupled to and energized by the stator outputs and of a resistivity in each region which varies as a function of position within the region with respect to a reference position in accordance with a cotangent function.
 2. A synchro system as defined in claim 1, wherein the stator comprises a square-shaped resistive material, three wipers of equal lengths connected to and spaced 120* about an axis of rotation, the wipers constituting the outputs of the stator, and means applying an input signal to two opposing sides of the square-shaped material.
 3. A synchro system as defined in claim 2, wherein at least one of the remaining two sides of the square-shaped material is electrically grounded.
 4. A synchro system, comprising a synchro control transmitter having a movable rotor and three stator outputs, a potentiometer serving as and directly interchangeable with a synchro control transformer and which comprises a three-region resistive material, points of connection to the resistive material being coupled to the stator outputs of the synchro control transmitter, a movable rotor forming part of the potentiometer and having two contacting means for engaging the resistive material at spaced points thereon so as to pick off the potentials of the engaged points of resistive material, the resistivity of the material varying in each region as a function of position of the potentiometer rotor with respect to a reference position and in accordance with a cotangent function so that the output potentials picked off by the contacting means are equal when the potentiometer rotor is in a position with respect to a reference position corresponding to a similar position of the rotor of the synchro control transmitter with respect to a reference position in the control transmitter.
 5. A synchro system as defined in claim 1, wherein the resistive material comprises a plurality of segments, each of which has the same resistivity in accordance with a cotangent function as another segment.
 6. A synchro system as defined in claim 1, wherein the resistivity of the material is expressed substantially by the following formula: R ( 1/2 -( 3/6) ctn. (30*+ X))Rt wherein R is the resistivity at a position in the material, X is the displacement of this position in electrical degrees from a reference position at an end of a segment of the material, which segment represents 120 electrical degrees, and Rt is the open circuit resistance between the ends of the resistive segment.
 7. A synchro system as defined in claim 6, wherein the resistive material is formed from three 120-electrical-degree segments as defined in claim 22, the resistive material has three points of connection thereto which are spaced 120 electrical degrees from each other, and these three points of connection are coupled to the stator outputs of the synchro control transmitter.
 8. A synchro system as defined in claim 7, including a rotor having two wipers contacting the resistive segments and which are spaced 180 electrical degrees from each other. 